Polyolefins have been used in a variety of applications as insulating materials and accordingly many studies have been conducted toward improving the electrical breakdown strength of polyolefins. For example U.S. Pat. Nos. 3,445,394 and 3,542,684 describe methods for improving electrical breakdown strength by adding various kinds of additives to the polyolefins. However, such methods have many disadvantages in that the additives used do not show good compatibility with polyolefins and that the resultant polyolefin compositions do not exhibit satisfactory properties as insulating materials e.g., processibility, thermal stability, voltage stability, resistance to treeing which is a characteristic generally viewed as an early stage of dielectric break-down. Accordingly, a need exists to provide a novel polyolefin composition which has excellent properties as an electrical insulating material and which is free from the above described disadvantages of the prior art.